基于砂岩数字岩芯图像的渗透率模拟与粗化
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摘要
运用闵可夫斯基泛函,结合K-means聚类方法,对应用CT扫描获得的砂岩数字岩芯图像进行岩石类型的精细划分,将岩芯划分成为粗粒区、细粒区和过渡区,进而获得岩芯的精细分层。基于砂岩数字岩芯图像,应用岩芯驱替模拟变换法,模拟在不同驱替压力条件下岩芯中湿相与非湿相的分布状况。应用格子玻尔兹曼方法(LBM),对岩芯各个小层进行渗透率的计算模拟,并采用直接加权平均、回归各岩石类型孔-渗关系曲线以及去除薄层后回归各岩石类型孔-渗关系曲线3种方法,完成对岩芯渗透率参数的粗化,获得粗化后的渗透率参数和孔-渗关系曲线方程。
Digital core analysis based on micro-CT computed tomography provide a new approach in core samples' permeability numerical prediction. Firstly, Minkowski functionals is applied along with the K-means cluster analysis to separate the sandstone core sample gotten from the micro-CT computed tomography into distinct classes, well-sorted fine grain, well-sorted large grain and transition area in order to get the elaborate layer system. Secondly, capillary drainage transform is performed to simulate the distribution of wetting and non-wetting phases under different drainage pressures. Lastly, LBM method is operated based on the core layer system to model permeability of each layers and upscaling is applied based on the simulated results with 3 different ways: directly applying the average method on the prediction values, finding the correlation function of permeability and porosity with and without thin layers in order to get the upscaling values of permeability and correlation function of permeability and porosity.
Digital core analysis based on micro-CT computed tomography provide a new approach in core samples' permeability numerical prediction. Firstly, Minkowski functionals is applied along with the K-means cluster analysis to separate the sandstone core sample gotten from the micro-CT computed tomography into distinct classes, well-sorted fine grain, well-sorted large grain and transition area in order to get the elaborate layer system. Secondly, capillary drainage transform is performed to simulate the distribution of wetting and non-wetting phases under different drainage pressures. Lastly, LBM method is operated based on the core layer system to model permeability of each layers and upscaling is applied based on the simulated results with 3 different ways: directly applying the average method on the prediction values, finding the correlation function of permeability and porosity with and without thin layers in order to get the upscaling values of permeability and correlation function of permeability and porosity.
引文
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[29]Schulz V,Wargo E,Kumbur E.Pore-morphologybased simulation of drainage in porous media featuring a locally variable contact angle.Transport in Porous Media,2015,107(1):13?25
[2]Ritman E L.Current status of developments and applications of micro-CT.Annu Rev Biomed Eng,2011,13(5):31?52
[3]姚军,赵秀才,衣艳静,等.数字岩芯技术现状及展望.油气地质与采收率,2005,12(6):52?54
[4]Cnudde V,Boone M N.High-resolution X-ray computed tomography in geosciences:a review of the current technology and applications.Earth-Science Reviews,2013,123(1):1?17
[5]Helliwell J R,Sturrock C J,Grayling K M,et al.Applications of X-ray computed tomography for examining biophysical interactions and structural development in soil systems:a review.European Journal of Soil Science,2013,64(3):279?297
[6]Nakashima Y,Mitsuhata Y,Nishiwaki J,et al.Nondestructive analysis of oil-contaminated soil core samples by X-ray computed tomography and lowfield nuclear magnetic resonance relaxometry:a case study.Water,Air,and Soil Pollution,2011,214:681?698
[7]Sakellariou A,Sawkins T J,Senden T J,et al.X-ray tomography for mesoscale physics applications.Physica A:Statistical Mechanics and its Applications,2004,339(1/2):152?158
[8]Mavko G,Mukerji T,Dvorkin J.The rock physics handbook:tools for seismic analysis of porous media.Cambridge:Cambridge University Press,2009
[9]Arns C H,Knackstedt M A,Martys N.Cross-property correlations and permeability estimation in sandstone.Physical Review E,2005,72(4):046304
[10]孙海,姚军,张磊,等.基于孔隙结构的页岩渗透率计算方法.中国石油大学学报(自然科学版),2014,38(2):92?98
[11]王晨晨,姚军,杨永飞,等.基于格子玻尔兹曼方法的碳酸盐岩数字岩芯渗流特征分析.中国石油大学学报(自然科学版),2012,36(6):94?98
[12]王鑫,姚军,杨永飞,等.基于组合式平板模型预测曲面裂缝数字岩芯渗透率的方法.中国石油大学学报(自然科学版),2013,37(6):82?86
[13]Martys N S,Chen H.Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method.Physical Review E,1996,53(1):743?750
[14]Arns C H,Knackstedt M A,Pinczewski M V,et al.Accurate estimation of transport properties from microtomographic images.Geophysical Research Letters,2001,28(17):3361?3364
[15]Qian Y H,Zhou Y.Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation.EPL(Europhysics Letters),1998,42(4):359?364
[16]Qian Y,d’Humières D,Lallemand P.Lattice BGKmodels for Navier-Stokes equation.EPL(Europhysics Letters),1992,17(6):479?484
[17]Levitz P.Toolbox for 3D imaging and modeling of porous media:Relationship with transport properties.Cement and Concrete Research,2007,37(3):351?359
[18]Chen S,Doolen G D.Lattice Boltzmann method for fluid flows.Annual Review of Fluid Mechanics,1998,30(1):329?364
[19]Inamuro T,Ogata T,Tajima S,et al.A lattice Boltzmann method for incompressible two-phase flows with large density differences.Journal of Computational Physics,2004,198(2):628?644
[20]Mecke K R.Morphology of spatial patterns-porous media,spinodal decomposition and dissipative structures.Acta Physica Polonica B,1997,28(1):1747?1782
[21]Arns C H,Mecke J,Mecke K,et al.Second-order analysis by variograms for curvature measures of twophase structures.The European Physical Journal B:Condensed Matter and Complex Systems,2005,47(3):397?409
[22]Arns C H,Knackstedt M A,Pinczewski M V,et al.Euler-Poincarécharacteristics of classes of disordered media.Physical Review E,2001,63(3):031112
[23]Arns C H.The influence of morphology on physical properties of reservoir rocks[D].Sydeny:The University of New South Wales,2002
[24]Lloyd S.Least squares quantization in PCM.IEEETransactions on Information Theory,1982,28(2):129?137
[25]Ismail N I.Rock typing using the complete set of additive morphological descriptors[D].Sydney:The University of New South Wales,2014
[26]Adler P M.Porous media:geometry and transports.Boston:Butterworth-Heinemann,1992
[27]Hilfer R.Local-porosity theory for flow in porous media.Physical Review B,1992,45(13):7115?7121
[28]Arns C H.Morphy Uesr Guide.Sydeny:The University of New South Wales,2015
[29]Schulz V,Wargo E,Kumbur E.Pore-morphologybased simulation of drainage in porous media featuring a locally variable contact angle.Transport in Porous Media,2015,107(1):13?25